They don't really have a history. Mikado was solely a target Shirogane had after placing 2nd in the national mock exams under him, hence why the biggest sign on his room during the Iceguya arc was "DEFEAT MIKADO."
Also he'll probably play into the whole "defy the legend of Kaguya-hime" theme the manga has gone for so far since Mikado was the Emperor who tried to marry Kaguya-hime. Same with this new guy Abe likely aiming for Shiranui (fire rat) as per Kaguya's Impossible Tasks.
@Damnfrickyou He took first place in the national mock exams, as early as chapter 4. You can read about him in Maki's bio, and he also travelled to India with her.